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A simple experiment Question: – Does adding weight to a coin make it unfair? – Blu-tac added to head side Need to construct testable hypotheses – The null hypothesis

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Weighted coin toss Toss the coin 10 times What is the hypothesis about how you think your system will behave? – More likely to get heads – Less likely to get heads – Either more or less likely to get heads What are the corresponding null hypotheses? – That the coin is fair

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Behaviour of a fair coin The model is a fair 50:50 coin How do we generate information about how a fair coin behaves? – Toss an un-weighted coin 10 times and repeat

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Behaviour of weighted coin Compare the weighted coin against the expected behaviour of a fair coin Question – How likely is it that our observed coin is fair?

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Alternative hypotheses HA: coin is more likely to produce heads – One-tailed test in right tail HA: coin is less likely to produce heads – One-tailed test in left tail HA: coin is unfair (in either direction) – Two-tailed test including both left and right tails

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P-values A p-value is the probability of your observed data or more extreme being generated according to the null hypothesis The less likely your data are, the less likely you would accept the null hypothesis as being true – We generally use a cut-off of p<0.05 to accept the alternative hypothesis One or two tailed tests refer to where you predict your alternative hypotheses to lie before you do your experiment

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Summary Science is about constructing experiments or designing observations to test your ideas about how the world works Hypotheses must be falsifiable Generally we construct null hypotheses against which our alternative hypotheses can be tested p-values tell us how likely it is our data came from the null hypothesis and therefore allow us to accept or reject it (H0)